Convergence of invariant densities in the small-noise limit

Details Convergence of invariant densities in the small-noise limit Convergence of invariant densities in the small-noise limit

2004-06-09

arxiv.org/abs/math/0406201v2

Nonlinearity 18 (2005) 659-683

Mathematics

Dynamical Systems

27 pages, 19 figures, revised with minor corrections

Scientific paper

10.1088/0951-7715/18/2/011

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.

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